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If sqrt((log)2x)-0. 5=(log)2sqrt(x ,) th...

If `sqrt((log)_2x)-0. 5=(log)_2sqrt(x ,)` then `x` equals (a)odd integer (b) prime number composite number (d) irrational

A

odd integer

B

prime number

C

composite number

D

irrational

Text Solution

Verified by Experts

The correct Answer is:
B
`sqrt(log_(2)x)-0.5 = log_(2) sqrtx`
` or sqrt(log_(2)x)-0.5 = 0.5 log_(2)x`
` rArr y - 0.5 = 0.5y^(2)`
`rArr y^(2) - 2y + 1 = 0`
` rArr y = 1`
`rArr log_(2) x = 1`
` rArr x = 2`
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CENGAGE PUBLICATION-LOGARITHM AND ITS PROPERTIES-Exercises (Single Correct Answer Type)
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  20. If xy^(2) = 4 and log(3) (log(2) x) + log(1//3) (log(1//2) y)=1 , then...

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